Complex Analysis is a branch of mathematics that studies functions of complex numbers. Unlike real numbers, complex numbers have a real part and an imaginary part, allowing for a richer structure. This field explores how these functions behave, including concepts like continuity, differentiation, and integration, but in the context of complex variables. One of the key results in Complex Analysis is Cauchy's Integral Theorem, which states that the integral of a holomorphic function over a closed curve is zero. This theorem leads to powerful applications, such as Residue Theorem, which helps in evaluating complex integrals and solving real-world problems in physics and engineering.